arithmetic sequence (NUMNER SEQUENCE).pptx

An arithmetic sequence is a list of numbers where the difference between any two consecutive terms is constant. This constant difference is called the common difference, often denoted by the letter d.

1. Arithmetic Sequence An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant. This constant difference is called the common difference. In simpler terms, you get the next number in the sequence by adding or subtracting the same value repeatedly.

2. Find the COMMON DIFFERENCE with SOLUTION 1, 4, 7, 10, … 5, 12, 19, 26, 33 -1, -4, -7, -10, … 20, 17, 14, 11, 8 a, 2a + 1, 3a + 2, 4a +3, …

3. Sum of the Arithmetic Sequence The sum of an arithmetic sequence (or arithmetic series) is the sum of all its terms. Formulas: If you have an arithmetic sequence with; 2, 4, 6, 8, 10 First term  

4. Arithmetic Series Find the sum of the 6 term in a given sequence 4, 7, 10, 13, 16, 19 In a given sequence 10, 20, 30 40, … find the sum of the first 20 terms. Find the sum of the 12 terms in sequence 15, 12, 9, 6, . . .

5. Find the missing terms 5, 12, ___, 26, ____ 3,__ ,__ ,__ ,15 8, 5, __, -1, __ 3, __, __, __, -13

6. Arithmetic Means arithmetic means are the terms you insert between two numbers to maintain a constant difference between consecutive terms. Example: 2 , _____, _____,  8 Find the five arithmetic means between 47 and 5. Find the arithmetic mean between 8 and 16.

7. Lets Practice! Insert the indicated number of arithmetic means between the two numbers. Two, between 12 and 24 •12, ____, ____, 24 Three, between 16 and 32 •16, ____, ____, ____, 32 Four, between 8 and -2     •8, ____, ____, ____, ____, -2 Five, between 39 and 15 •39, ___, ___, ___, ___, ___, 15

8. More examples What is the first term and last term of an arithmetic sequence when its arithmetic means are 45, 25, 5, -15? If five arithmetic means are inserted between -9 and 9, what is the third term?

9. Quiz 2 Find the missing terms Two, between 6 and 30 •6, ____, ____, 30 Three, between 8 and -4     •8, ____, ____, ____, -4 The arithmetic mean between two terms in an arithmetic sequence is 9. If one of these terms is 12, find the other term. Form a sequence that has three arithmetic means between 38 and 54.